Brantley tosses a ball out of a window that is 75 feet in the air. Its initial velocity is 12 feet per second. The path of the ball is represented by h=-16t^2+12t+75. How long does it take for the ball to hit the ground to the nearest hundredth?

Step-by-step explanation:

Given

Required

Determine the time to hit the ground

The ground is at point 0.

So, to solve this; we simply set , then calculate the value of t

Multiply through by -1

Reorder

Solve using quadratic formula:

Where

Split:

or

or

But time (t) can't be negative;

So, we make use of only

Hence, the time to hit the ground is 2.57 seconds

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743